Trump didn't dismiss the possibility of keeping Yellen, a liberal Democrat, and recounted a meeting he had with her, three days ago.

"She was very impressive, I like her a lot," Trump said. "It's somebody that I am thinking about."

Trump has reportedly been teasing picks to head the Fed in recent days. Two candidates — Jerome Powell, a former private equity magnate now on the Fed's board; and Kevin Warsh, a former Fed governor and Morgan Stanley banker — are considered to be leading the pack.